^{1} Theoretical Particle Physics and Cosmology, The Niels Bohr Institute, Faculty of Science, Københavns Universitet^{2} Princeton University^{3} Theoretical Particle Physics and Cosmology, The Niels Bohr Institute, Faculty of Science, Københavns Universitet

DOI:

10.1103/PhysRevLett.113.161601

Abstract:

he classical Kepler problem, as well as its quantum mechanical version, the hydrogen atom, enjoys a well-known hidden symmetry, the conservation of the Laplace-Runge-Lenz vector, which makes these problems superintegrable. Is there a relativistic quantum field theory extension that preserves this symmetry? In this Letter we show that the answer is positive: in the nonrelativistic limit, we identify the dual conformal symmetry of planar N=4 super Yang-Mills theory with the well-known symmetries of the hydrogen atom. We point out that the dual conformal symmetry offers a novel way to compute the spectrum of bound states of massive W bosons in the theory. We perform nontrivial tests of this setup at weak and strong coupling and comment on the possible extension to arbitrary values of the coupling.